The band is breaking up and Rob, Sue, Tim and Vito each want the tour bus. Using the method of sealed bids, Rob bids $4300, Sue bids $5900, Tim bids $3500, and Vito bids $6200 for the bus. Since Vito's bid is the highest, he gets the bus and has to compensate the others to make the division fair. How much money will Rob get from Vito? Be sure to compute your answer to the nearest cent.

To determine how much Rob, Sue, and Tim should get from Vito using the method of sealed bids, we will follow these steps:

### Step 1: Calculate the total of all the bids.
The total bids from all four individuals are:
\[
4300 + 5900 + 3500 + 6200 = 19900
\]

### Step 2: Calculate the fair share for each person.
The fair share for each person is computed by dividing the total bid by the number of people (4):
\[
\text{Fair share for each person} = \frac{19900}{4} = 4975
\]

### Step 3: Determine how much Vito must pay.
Vito's bid for the bus was \$6200, which is more than his fair share of \$4975. Therefore, he must compensate the other three to make the division fair.

### Step 4: Compute the compensation to Rob.
Since Vito's bid exceeded his fair share by:
\[
6200 - 4975 = 1225
\]
Vito must compensate Rob, Sue, and Tim by distributing this amount in proportion to their fair shares. 

To determine how much Rob will receive, we subtract his fair share from his bid:
\[
\text{Rob's bid} = 4300, \quad \text{Rob's fair share} = 4975
\]
Rob's shortfall is:
\[
4975 - 4300 = 675
\]

### Step 5: Vito compensates Rob.
Vito will give Rob the shortfall amount, which is:
\[
\boxed{675 \text{ dollars}}
\]

Thus, Rob will receive \$675 from Vito.

Would you like further details or have any questions? Here are five related questions you might find interesting:

1. How much will Sue receive from Vito?
2. What is Tim's compensation in this scenario?
3. What would happen if someone bids less than their fair share?
4. How can we ensure that the method of sealed bids is fair for everyone involved?
5. How is this method applied in other real-world situations like estate divisions?

**Tip:** The sealed bids method is often used to fairly divide assets when people have different valuations of them!

Learn how to apply the sealed bids method to divide assets fairly. In this example, Vito wins the tour bus with a bid of $6200 and compensates the others. See how Rob's compensation of $675 is calculated using fair share principles. Suitable for students in Grades 9-12.

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